Materials 2013, 6, 5613-5624; doi:10.3390/ma6125613
OPEN ACCESS
materials
ISSN 1996-1944
www.mdpi.com/journal/materials
Article
A Compact Band-Pass Filter with High Selectivity and Second
Harmonic Suppression
Ramona Cosmina Hadarig *, Maria Elena de Cos Gomez and Fernando Las-Heras
Signal Theory and Communications Area, Department of Electrical Engineering, University of
Oviedo, Multi-Purpose Building, Module 8, Gijón 33203 (Asturias), Spain;
E-Mails: medecos@tsc.uniovi.es (M.E.C.G.); flasheras@tsc.uniovi.es (F.L.-H.)
* Author to whom correspondence should be addressed; E-Mail: rhadarig@tsc.uniovi.es.
Received: 3 October 2013; in revised form: 6 November 2013 / Accepted: 19 November 2013 /
Published: 3 December 2013
Abstract: The design of a novel band-pass filter with narrow-band features based on an
electromagnetic resonator at 6.4 GHz is presented. A prototype is manufactured and
characterized in terms of transmission and reflection coefficient. The selective passband
and suppression of the second harmonic make the filter suitable to be used in a C band
frequency range for radar systems and satellite/terrestrial applications. To avoid substantial
interference for this kind of applications, passive components with narrow band features
and small dimensions are required. Between 3.6 GHz and 4.2 GHz the band-pass filter with
harmonic suppression should have an attenuation of at least 35 dB, whereas for a passband,
less than 10% is sufficient.
Keywords: band-pass filter; artificial magnetic conductor; dispersion diagram; second
harmonic suppression; transmission coefficient
1. Introduction
In recent years, emerging applications have continued to challenge radio frequency (RF)/microwave
filters’ designers with stringent simultaneous requirements such as high performance, light weight, low
cost and miniaturization. As the electromagnetic spectrum is limited and has to be shared, small sized
band-pass filters with narrow frequency response and high selectivity are used to confine the signals
within assigned spectral limits and to reject the noise and interferences from adjacent channels.
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To minimize the filter size, a practical strategy is to reduce the resonator circuit by modifying its
physical structures [1–7]. Starting from the conventional parallel coupled band-pass filter [8–11] which
has a simple synthesis procedure, and ending with U-shape resonators and open loops [12,13], hairpin
filters [14] has helped progress in size reduction. However, with the rapid evolution of modern
communication systems [15], the sizes of these resonators are still not small enough to be used.
In this work, a novel low thickness band-pass filter based on a simple and compact size
electromagnetic resonator without vias is presented. The novelty of this contribution relies on taking
advantage of the predicted electromagnetic band-gap (EBG) properties of a resonator unit-cell with
improved performance (by means of its dispersion diagram) to achieve the intended band-pass filter
behavior. Moreover, the filter exhibits a narrow passband, high out-of-band rejection level, and second
harmonic suppression. The paper is organized as follows. Section 2 outlines the study of the unit-cell
resonator in terms of dispersion diagram. In Section 3, the design of the filter is presented based on the
unit-cell resonator. Also, the possibility of suppressing of the second harmonic is discussed. Two
filters are manufactured and measurements concerning the transmission coefficient are provided to
show their performance results.
2. Resonant Element Design
The first step in the design of the band-pass filter (henceforth referred to as BPF) is the design of
the resonant element. In [16], the resonant element—replicated to model an infinite resonant
structure—is characterized as an Artificial Magnetic Conductor (AMC) material [17–20] and the
in-phase reflection property was studied. This feature enables efficient radiation for antennas placed
closed to the periodic structure. In this contribution the resonant structure is seen from another point of
view: as a material that has the possibility to block the propagation of electromagnetic waves in certain
frequency bands and guide them in a desired direction [i.e., electromagnetic band-gap (EBG)].
EBG structures [21,22] exhibit allowed and forbidden bands of modes’ propagation and can be
characterized by the dispersion diagram. The dispersion diagram for a unit-cell of period W will show
the relation between the wave number and frequency, giving information about the propagating modes
and band-gaps that can potentially exist between such modes [23,24]. The eigenmode solver of High
Frequency Structural Simulator (HFSS) together with proper boundary conditions along the sides of
the unit-cell (resembling an infinite structure) is used in order to determine the dispersion diagram of
the structure (see Figure 1a). Due to symmetry of the unit-cell, the dispersion diagram is computed
along the lines connecting the R, X and M points, to form the irreducible Brillouin triangle. Thus the
dispersion analysis of periodic structures is reduced to find only the propagation modes in the direction
of the vectors of the irreducible Brillouin triangle. The dispersion characteristics, i.e., the position and
width of the band-gap and the frequency of the propagating modes are primarily defined by the
geometry of the unit-cell. ARLON25N with relative dielectric permittivity 3.28, loss tangent less than
0.0025 and a thickness of 0.762 (30 mils) is used as dielectric substrate. The unit-cell dimensions are
W × W = 11.52 mm × 11.52 mm and its geometry exhibits four symmetry planes. The metallization
thickness is 18 μm.
The dispersion diagram for three lowest modes is depicted in Figure 1b. The first mode propagates
in the frequency range from 5 to 6.6 GHz, whereas the second mode propagates from 5 to 7 GHz.
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The resonance frequency takes place between the first and second mode, being around 6 GHz.
Moreover, the bandgap is presented in a frequency range from 7 to 7.8 GHz. Within the bandgap, the
electromagnetic waves cannot propagate at any direction in the EBG structure.
Figure 1. (a) Unit-cell resonator. The applied boundary conditions with the irreducible
Brillouin triangle; and (b) Dispersion diagram of the periodic structure.
3. Filter Design
With the purpose of designing a band-pass filter having the same size as the unit-cell resonator, the
propagation mode paths along the R-X-M triangle and predicted by the dispersion diagram could be
followed. The frequency of the modes propagating along the edges of the Brillouin triangle have to be
taken into account to define the filter passband, whereas the band-gap can be used to achieve the filter
stopband. The computed dispersion diagram shows the propagation of the first mode in the frequency
range from 5 to 6.6 GHz. In the present work, only the (M-R) region and part of the (X-M) region from
the dispersion diagram were considered due to the fact that the authors’ goal was to obtain a selective
band-pass filter.
The distance between the metallization edge and the unit-cell edge influences the band-gap position.
More precisely when the mentioned distance increases, the band-gap shifts to a higher frequency band
whereas its width increases. The variation of the a2 and a3 parameters (see Figure 2) has the following
effect: as a2 and a3 increase the band-gap shifts to a lower frequency band whereas the width of the
band-gap increases. When a1 and a4 parameters decrease, meaning that the whole unit-cell size
decreases, the band-gap shifts to a higher frequency band and its width increases. The thickness of the
dielectric substrate also has an influence on the band-gap position. Increasing the thickness, the
band-gap shifts to a lower frequency band and in the same time its width increases.
The filter consists of a unit-cell resonator and two narrow lines coupled to the resonator. Each
narrow line has a width of 0.1 mm and a length of 11.52 mm. The two narrow lines are placed
symmetrically with respect to the unit-cell resonator. The gap between the coupling narrow line and
unit-cell resonator is 0.1 mm. The filter is excited by a pair of non-orthogonal input/output 50 Ω
microstrip feeding lines of 1.8 mm width and is printed on an ARLON25N substrate with a thickness
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of 30 mils, relative dielectric permittivity of 3.28, cooper thickness 18 μm and loss tangent 0.0025. The
layout of the filter in 6.4 GHz frequency band is presented in Figure 2.
Figure 2. Layout of the band-pass filter (BPF) with its characteristic circuit model.
In order to determine the characteristics of the BPF, two approaches could be followed. The first
one is to model the BPF using its equivalent circuit (or at least a simplified version) as can be seen in
Figure 2. The resonator unit-cell can be model based on transmission line theory [25] providing that
the unit-cell size is electrically small enough. The presented unit-cell is λ0/5 so it can be considered not
so small and being at the limit of application of such a model. In any case the model would comprise a
series connection (L2 and C2) in parallel with the equivalent impedance of the parallel L3 and C3
components. In series with the mentioned circuit the capacitance C1 (formed between the resonator and
each narrow coupling line) and Ll and R components (modeling the transmission line) are placed. The
second approach consists in explaining the physical phenomena under the filter behavior. To achieve
this aim the modes propagation in the structure should be explained based on dispersion diagram so the
second approach is followed.
The dimensions of the filter are 29.8 × 11.52 × 0.762 mm3 (0.64λ0 × 0.25λ0 × 0.016λ0, λ0 is the
free space wavelength, λ0 = 47 mm at 6.4 GHz) considering the input/output feeding lines and
11.92 × 11.52 × 0.762 mm3 (0.25λ0 × 0.25λ0 × 0.016λ0) without the input/output feeding lines. From
simulation results in Figure 3a, the 3dB passband of BPF without harmonic suppression goes from
6.25 to 6.62 GHz, meaning 5.75% fractional bandwidth at the center frequency 6.44 GHz. The
minimum insertion loss is 1.7 dB whereas the maximum return loss value is greater than 17 dB (see
Figure 3b).
Figure 3. (a) Simulation vs. measurement: Transmission coefficient of the BPF;
(b) Simulation vs. measurement: Reflection coefficient of the BPF.
a)
b)
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Taking into account the position of the feeding lines with respect to the unit-cell geometry, the
propagation follows a quasi-diagonal path, which coincides with the (M-R) region from the dispersion
diagram as being together with part of the (X-M) region. Furthermore, from the (M-R) region, as well
as part of the (X-M) region of the dispersion diagram resulted in the first mode propagating in a
frequency spectrum of between 6 and 6.6 GHz. This band corresponds to the electromagnetic wave
propagation through the BPF geometry whereas from 6.94 to 7.9 GHz the structure does not allow any
mode propagation which corresponds to the stopband frequency region of the BPF.
In Table 1, the 3 dB bandwidth together with the quality factor are presented. In a band-pass filter,
the overall width of the passband between the upper and lower 3 dB levels of the filter determines the
quality factor Q. The lower the value of the Q factor, the wider the bandwidth and, consequently, the
higher the Q factor, the narrower and more selective the filter.
Table 1. Simulated band-pass filter quality factor.
3 dB
flow(GHz) fhigh(GHz)
BPF
6.25
6.62
3-cells-oy BPF
6.45
6.61
3-cells-ox BPF
6.55
6.67
Square BPF
6.13
7.30
Prototype
fc
6.44
6.52
6.62
6.70
BW(3 dB)
Size
Q
(mm × mm)
GHz %
0.37 5.57 17.40 29.80 × 11.52 *
0.16 2.45 40.75 29.80 × 34.56 *
0.12 1.81 55.16 52.84 ×11.52*
1.17 17.4 5.72 29.80 ×11.52*
Size
(mm × mm)
11.92 × 11.52
11.92 × 34.56
34.96 × 11.52
11.92 × 11.52
* Considering the input/output feeding lines.
According to the analysis shown in Table 1, if three resonators are cascaded in the OY direction
(henceforth referred to as 3-cells-oy BPF) the 3 dB passband goes from 6.45 to 6.61 GHz, meaning
2.45% fractional bandwidth at the center frequency 6.52 GHz, whereas in the OX direction (filter
henceforth referred to as 3-cells-ox BPF) the 3 dB passband goes from 6.55 to 6.67 GHz, meaning
1.8% fractional bandwidth at the center frequency 6.62 GHz. Moreover, using three cells in the
direction of the current flow, the filter becomes more selective (see Figure 4a). The increment in the
number of unit-cells in the OY direction has an influence only in the passband of the filter, which
becomes narrower; meanwhile the slope in the stop bands remains the same. The benefit of the novel
BPF over the square shaped resonator BPF is a quality factor three times greater. Figure 4b shows that
the return loss increases with the number of unit-cells.
Figure 4. (a) S21 simulation results; and (b) S11 simulation results.
a)
b)
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In order to suppress the second harmonic, several techniques have been reported in literature.
In [26] two quarter wavelength open ended stubs are attached at the edges of the resonators in the main
coupling path in order to have harmonic suppression, but this implies additional circuit elements
against compact filter design. Another interesting alternative, such as using a continuous modulation in
the coupled section of the filter [27,28] and using Koch fractal geometry [29], have also been
considered, but both are time consuming due to the need of many parameters optimization. In this
contribution, defected ground structures (DGS) are used to act as a low-pass filter. The slots are placed
in the ground plane, directly under the input/output feeding lines [30].
The dimensions of the slots were chosen as c = 6.6 mm, d = 5 mm, f = 1.3 mm, g = 0.4 mm,
l = 4.8 mm, m = 4.4 mm, n = 1.3 mm, x = 1.6 mm, y = 1.9 mm (see Figure 5a). The conductor strip of the
microstrip line on the top plane has a width of 1.8 mm, corresponding to 50 Ω characteristic impedance.
From simulation results in Figure 5b, the DGS structure under the microstrip transmission line
exhibits a 3 dB cutoff frequency at 7.15 GHz and a center frequency of the stop band at 8.25 GHz with
a maximum attenuation of 33 dB.
Figure 5. (a) Topology of defected ground structures (DGS) section (bottom view); and
(b) transmission coefficient of DGS section.
a)
b)
The dimensions of the slots placed in the ground plane influence the 3 dB cutoff frequency and the
attenuation. Figure 6 shows the parametric study of the most important parameters “x”, “l”, “m” and
“c”. Only one parameter is changed at a time during the analysis. By increasing the “x” parameter, the
3 dB cutoff frequency decreases whereas the attenuation is almost the same at 8.25 GHz. The “l”
parameter controls both the attenuation at the center frequency of the stopband and the 3 dB cutoff
frequency. On decreasing “l”, the center frequency of the stopband, the attenuation and the 3 dB cutoff
frequency increase. The parameters “c” and “m” influence only the 3 dB cutoff frequency. The 3 dB
cutoff frequency decreases when the parameters “c” and “m” decrease.
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Figure 6. Parametric analysis of the DGS.
4. Results
Prototypes of the band-pass filter with second harmonic suppression (henceforth referred to as
BPF-DGS) and without harmonic suppression using one unit-cell resonator, have been manufactured
using laser micromachining (see Figure 7).
The results of measured transmission coefficient for the BPF-DGS and BPF prototypes are depicted
in Figure 8a. The measured 3 dB bandwidth goes from 6.16 to 6.62 GHz, signifying 460 MHz (7.18%)
for the BPF prototype. There is good agreement between measurement and simulation results for the
filter without harmonic suppression.
Regarding the BPF-DGS prototype, a 3 dB passband of 210MHz (3.32%) at the center frequency
6.32 GHz is obtained in simulation whereas, in measurements, 175 MHz (2.76%) passband at 6.33 GHz
resulted. In the stopband regions some slightly differences between measurement and simulation can
be observed. The fact that commercial MoM software considers infinite extension of the dielectric
substrate, together with manufacturing process tolerances and cables’ and connectors’ losses, explains
the differences in the stopband region. Nevertheless, the simulations and measurement results are in
good agreement and they meet the application requirements in the C band range. The filter with DGS
exhibits approximately 50% less pass bandwidth than the BPF without harmonic suppression because
of the reduced coupling generated.
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Figure 7. Manufactured prototype band-pass filter with second harmonic suppression
(BPF-DGS) (a) top view; (b) bottom view; and (c) cross-section view.
Figure 8. (a) S21 simulation and measurement results; and (b) S11 simulation and
measurement results.
a)
b)
The absence of multilayer substrates and vias make the filters suitable to be used not only in
satellite/terrestrial communication applications, but also in wearable applications where the prototypes
could be shape adapted and bended. From Table 2, it can be easily seen that the size of the proposed
BPF is minimized compared to band-pass filters with similar performance and substrate as used
in [31–34], whereas the BPF-DGS shows a higher quality factor.
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Table 2. Comparison with other band-pass filters.
Prototype
3 dB
flow (GHz) fhigh (GHz)
fc
BW(3 dB)
GHz
%
Q
BPF
6.25
6.62
6.44
0.37
5.75
17.40
BPF-DGS
[31]
[35]
[35]
[36]
[32]
[33]
[34]
[37]
[38]
[39]
[40]
6.23
5.46
5.58
5.39
5.88
6.63
5.09
5.14
4.78
5.54
1.36
2.84
6.40
5.84
5.83
6.02
6.12
6.96
5.35
5.38
5.61
5.86
1.49
4.2
6.33
5.65
5.71
5.71
6
6.8
5.25
5.25
5.2
5.7
1.42
3.4
0.17
0.38
0.25
0.63
0.24
0.33
0.26
0.24
0.83
0.32
0.13
1.36
2.76
6.72
4.46
11.14
4.05
4.9
4.9
4.57
16
5.6
9
40
36.38
14.80
22.80
9.06
25
20.6
20.2
21.8
6.26
17.81
10.9
2.5
Size
(mm × mm)
Size λ—wavelength
at the corresp. fc
29.8 × 11.52 *
11.92 × 11.52
29.8 × 11.52
46.2 × 11.5
40 × 10
40 × 10
15 × 13
20 × 22
45 × 14
19.8 × 17.9
26.3 × 9.9
26 × 8
22.14 × 5.08
20 × 15
0.63λ × 0.25λ *
0.25λ × 0.25λ
0.63λ × 0.25λ
0.87λ × 0.21λ
0.76λ × 0.19λ
0.76λ × 0.19λ
0.3λ × 0.26λ
0.45λ × 0.5λ
0.79λ × 0.25λ
0.35λ× 0.31λ
0.45λ × 0.17λ
0.5λ × 0.15λ
0.1λ × 0.023λ
0.22λ × 0.17λ
* Considering the input/output feeding lines.
The miniaturized BPF-DGS is demonstrated at 6.33 GHz, which is a higher frequency than the
reported filter in [35]. If the proposed filter would be made to operate in the same frequency band as
in [35], the filter would have a smaller size compared to [35].
In [37], the proposed filter renders a quality factor of 6.26, which is approximately three or six
times lower compared to 17.4 of the BPF and 36.38 of the BPF-DGS. In [39], the upper conducting
layer of the filter is connected through the bottom ground plane using vias. Even though in [39] a
0.1λ0 × 0.023λ0 miniaturized band-pass filter is shown, with a lower quality factor, it has the
disadvantage of high cost and a difficult manufacture process due to the use of vias which are
vulnerable to environmental influences such as being insufficiently plated through or filled with solder.
This may cause the delamination or cracking of the vias.
5. Conclusions
The design of a frequency selective band-pass filter with small dimensions and second harmonic
suppression using an electromagnetic resonator has been presented. A prototype has been
manufactured at 6.4GHz and characterized based on transmission loss measurements. Second
harmonic suppression was obtained using a DGS topology. The filter presents a high selectivity with a
sharp passband to stop band transition. The compact size, low cost, simple fabrication and integration
with other components in the system make it appropriate for satellite/terrestrial communication and
wearable applications.
Acknowledgments
This work has been supported by the Ministerio de Ciencia e Innovación of Spain/FEDER under
projects TEC2011-24492 (ISCAT) and CONSOLIDER-INGENIO CSD2008-00068 (TERASENSE),
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by the Gobierno del Principado de Asturias (PCTI)/FEDER-FSE under projects PC10-06
(FLEXANT), by grant BP10-039.
Conflicts of Interest
The authors declare no conflict of interest.
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